Probabilistic Cluster Unfoldings for Petri Nets

This article introduces a probabilistic unfolding semantics for untimed Petri nets. No structural or safety assumptions are made. We show that cluster semantics is an adequate framework for the construction of probability measures for concurrent runs. The unfolding semantics is constructed by local choices on each cluster, and a distributed scheduling mechanism (cluster net) authorizing cluster actions. The probability measures for the choice of step in a cluster are obtained by constructing Markov Fields on the conflict graph of transitions, from suitable Gibbs potentials. We introduce and characterize stopping times for these models, and a strong Markov property